sysdeps/powerpc/fpu/e_sqrtf.c

   1 /* Single-precision floating point square root.
   2    Copyright (C) 1997-2015 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 #include <math.h>
  20 #include <math_private.h>
  21 #include <fenv_libc.h>
  22 #include <inttypes.h>
  23 #include <stdint.h>
  24 #include <sysdep.h>
  25 #include <ldsodefs.h>
  26
  27 #ifndef _ARCH_PPCSQ
  28 static const float almost_half = 0.50000006;    /* 0.5 + 2^-24 */
  29 static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
  30 static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
  31 static const float two48 = 281474976710656.0;
  32 static const float twom24 = 5.9604644775390625e-8;
  33 extern const float __t_sqrt[1024];
  34
  35 /* The method is based on a description in
  36    Computation of elementary functions on the IBM RISC System/6000 processor,
  37    P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
  38    Basically, it consists of two interleaved Newton-Raphson approximations,
  39    one to find the actual square root, and one to find its reciprocal
  40    without the expense of a division operation.   The tricky bit here
  41    is the use of the POWER/PowerPC multiply-add operation to get the
  42    required accuracy with high speed.
  43
  44    The argument reduction works by a combination of table lookup to
  45    obtain the initial guesses, and some careful modification of the
  46    generated guesses (which mostly runs on the integer unit, while the
  47    Newton-Raphson is running on the FPU).  */
  48
  49 float
  50 __slow_ieee754_sqrtf (float x)
  51 {
  52   const float inf = a_inf.value;
  53
  54   if (x > 0)
  55     {
  56       if (x != inf)
  57         {
  58           /* Variables named starting with 's' exist in the
  59              argument-reduced space, so that 2 > sx >= 0.5,
  60              1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
  61              Variables named ending with 'i' are integer versions of
  62              floating-point values.  */
  63           float sx;             /* The value of which we're trying to find the square
  64                                    root.  */
  65           float sg, g;          /* Guess of the square root of x.  */
  66           float sd, d;          /* Difference between the square of the guess and x.  */
  67           float sy;             /* Estimate of 1/2g (overestimated by 1ulp).  */
  68           float sy2;            /* 2*sy */
  69           float e;              /* Difference between y*g and 1/2 (note that e==se).  */
  70           float shx;            /* == sx * fsg */
  71           float fsg;            /* sg*fsg == g.  */
  72           fenv_t fe;            /* Saved floating-point environment (stores rounding
  73                                    mode and whether the inexact exception is
  74                                    enabled).  */
  75           uint32_t xi, sxi, fsgi;
  76           const float *t_sqrt;
  77
  78           GET_FLOAT_WORD (xi, x);
  79           fe = fegetenv_register ();
  80           relax_fenv_state ();
  81           sxi = (xi & 0x3fffffff) | 0x3f000000;
  82           SET_FLOAT_WORD (sx, sxi);
  83           t_sqrt = __t_sqrt + (xi >> (23 - 8 - 1) & 0x3fe);
  84           sg = t_sqrt[0];
  85           sy = t_sqrt[1];
  86
  87           /* Here we have three Newton-Raphson iterations each of a
  88              division and a square root and the remainder of the
  89              argument reduction, all interleaved.   */
  90           sd = -__builtin_fmaf (sg, sg, -sx);
  91           fsgi = (xi + 0x40000000) >> 1 & 0x7f800000;
  92           sy2 = sy + sy;
  93           sg = __builtin_fmaf (sy, sd, sg);     /* 16-bit approximation to
  94                                                    sqrt(sx). */
  95           e = -__builtin_fmaf (sy, sg, -almost_half);
  96           SET_FLOAT_WORD (fsg, fsgi);
  97           sd = -__builtin_fmaf (sg, sg, -sx);
  98           sy = __builtin_fmaf (e, sy2, sy);
  99           if ((xi & 0x7f800000) == 0)
 100             goto denorm;
 101           shx = sx * fsg;
 102           sg = __builtin_fmaf (sy, sd, sg);     /* 32-bit approximation to
 103                                                    sqrt(sx), but perhaps
 104                                                    rounded incorrectly.  */
 105           sy2 = sy + sy;
 106           g = sg * fsg;
 107           e = -__builtin_fmaf (sy, sg, -almost_half);
 108           d = -__builtin_fmaf (g, sg, -shx);
 109           sy = __builtin_fmaf (e, sy2, sy);
 110           fesetenv_register (fe);
 111           return __builtin_fmaf (sy, d, g);
 112         denorm:
 113           /* For denormalised numbers, we normalise, calculate the
 114              square root, and return an adjusted result.  */
 115           fesetenv_register (fe);
 116           return __slow_ieee754_sqrtf (x * two48) * twom24;
 117         }
 118     }
 119   else if (x < 0)
 120     {
 121       /* For some reason, some PowerPC32 processors don't implement
 122          FE_INVALID_SQRT.  */
 123 #ifdef FE_INVALID_SQRT
 124       feraiseexcept (FE_INVALID_SQRT);
 125
 126       fenv_union_t u = { .fenv = fegetenv_register () };
 127       if ((u.l & FE_INVALID) == 0)
 128 #endif
 129         feraiseexcept (FE_INVALID);
 130       x = a_nan.value;
 131     }
 132   return f_washf (x);
 133 }
 134 #endif /* _ARCH_PPCSQ  */
 135
 136 #undef __ieee754_sqrtf
 137 float
 138 __ieee754_sqrtf (float x)
 139 {
 140   double z;
 141
 142 #ifdef _ARCH_PPCSQ
 143   asm ("fsqrts  %0,%1\n" :"=f" (z):"f" (x));
 144 #else
 145   z = __slow_ieee754_sqrtf (x);
 146 #endif
 147
 148   return z;
 149 }
 150 strong_alias (__ieee754_sqrtf, __sqrtf_finite)